Curves of the form $\displaystyle y=\frac{ax+b}{cx+d}$ can be written as $\displaystyle y = A + \frac{B}{cx+d}$.
They have asymptotes $y=A$ and $\displaystyle x = - \frac{d}{c}$.

Examples

Other points of note

We have focused most of our attention on asymptotes as they are newer concepts.

Graphing calculators can be used to help us determine the shapes of our curves.

Concept check: do you recall how to find the coordinates of the axial intercepts?